Selecting bit positions for storing a digital watermark

ABSTRACT

A method comprises selecting bit positions for storing a digital watermark in digital audio data in time domain by choosing a spread function characterising the plurality of the selected bit positions, wherein the spread function comprises at least one Gaussian curve.

TECHNICAL FIELD

The present invention relates to a method and a system for selecting bitpositions for storing a digital watermark in digital data, and inparticular selecting bit positions corresponding to a predeterminedspread function.

BACKGROUND OF THE INVENTION

Because of the increased interest in protecting digital data fromillegal copying, watermarking of data has, in recent years, becomeincreasingly popular. Embedding a watermark into a digital data fileinvolves selecting samples from the digital data file and recording inselected bits of these samples, data comprising copyright information.Arrangements can then be made so that any unauthorized access or copyingof the original data file runs the risk of the extracted watermarkexposing the lack of legal ownership of the file.

An official and reliable watermark has to be difficult to find andremove or override. In addition, the watermark should not affectsubstantially the quality of the original data file.

Copyright protection by way of watermarking has become especiallypopular in the music industry, where recently there has been a strongincrease in illegal downloads and copying. For the process ofwatermarking audio files, however, an additional consideration isrelated to the fact that many such files, together with the embeddedwatermarks, are processed on mobile phones and other hand-held players.In order to minimize cost and extend battery life, such hand-helddevices often have slow processors with limited computationalcapabilities.

Some of the methods developed for embedding watermarks use spreadspectrum techniques in the frequency domain. These methods generallyrequire the original audio data for watermark detection. These methodsalso are computationally intense, because of the complex transformationsinvolved in the data processing. Accordingly, these methods are notsuitable for processing watermarked files in hand-held devices.

Other techniques embed watermarks in the time domain. Many of thesetechniques use the least significant data bits of the respective datasamples to store the watermark. One disadvantage of this approach isthat the stored watermark can be erased without significantly erodingthe audio quality, thus undermining the reliability of the protection.

Accordingly, it is desirable to develop a method for embedding awatermark in digital data that is tamper-resistant and relativelysimple, so that the verification of the watermark would not requiresubstantial computational capabilities.

SUMMARY OF THE INVENTION

According to a first aspect of the invention, there is provided a methodfor protecting digital audio data comprising a plurality of samples. Themethod comprises selecting bit positions for storing a digital watermarkin the digital audio data in time domain, by choosing a spread functioncharacterising the plurality of the selected bit positions, wherein thespread function comprises at least one Gaussian curve.

Preferably, the at least one Gaussian curve is defined by spreadfunction parameters including;

-   -   the point of time corresponding to the peak of the Gaussian        curve,    -   the standard deviation of the Gaussian curve;    -   the time interval between samples selected for storing the        watermark; and    -   the bit position of the sample storing the watermark at the peak        of the Gaussian curve.

According to a second aspect of the invention, there is provided astand-alone or a networked computer system for selecting bit positionsfor storing a watermark in a digital audio signal, the signal comprisingof plurality of samples in time domain. The computer system comprisescomputational means for spreading the digital watermark data in timedomain by storing the data in bit positions of selected ones of thesamples. The computational means are programmed to define a spreadfunction characterising the plurality of the selected bit positions usedfor storing the watermark. The spread function comprises at least oneGaussian curve defined by spread parameters including;

-   -   the point of time corresponding to the peak of the Gaussian        curve;    -   the standard deviation of the Gaussian curve;    -   the time interval between samples selected for storing the        watermark; and    -   the bit position of the sample storing the watermark at the peak        of the Gaussian curve.

According to a third aspect of the invention, there is provided acomputer program product comprising a computer readable medium with acomputer program recorded therein for selecting bit positions forstoring a watermark in a digital audio data in time domain. The digitaldata comprises a plurality of samples. The computer program comprisesmeans for spreading the digital watermark data by storing the data inbit positions of selected ones of the samples. The spread functioncharacterising the plurality of the selected bit positions used forstoring the watermark comprises at least one Gaussian curve defined byspread parameters including;

-   -   the point of time corresponding to the peak of the Gaussian        curve;    -   the standard deviation of the Gaussian curve;    -   the time interval between samples selected for storing the        watermark; and    -   the bit position of the sample storing the watermark at the peak        of the Gaussian curve.

BRIEF DESCRIPTION OF THE DRAWINGS

In the drawings:

FIG. 1 is a schematic diagram of a spread function of one embodiment ofthe present invention applied to a digital audio signal.

FIG. 2 is a schematic flow diagram of a process of selecting the bitpositions for storing the water mark, embodying the invention.

FIG. 3 is a detailed process diagram of the process of selecting the bitpositions for storing the water mark shown in FIG. 2.

FIG. 4 is a schematic diagram of a computer system for implementingembodiments of the invention.

DETAILED DESCRIPTION

Method, system and computer program products for selecting bit positionsfor storing a digital watermark are described. In the following detaileddescription of exemplary embodiments of the invention, reference is madeto the accompanying drawings that form a part hereof, and in which isshown by way of illustration specific exemplary embodiments in which theinvention may be practiced. These embodiments are described insufficient detail to enable those skilled in the art to practice theinvention. Other embodiments may be utilized, and logical, mechanical,and other changes may be made without departing from the spirit or scopeof the present invention. The following detailed description is,therefore, not to be taken in a limiting sense, and the scope of thepresent invention is defined only by the appended claims.

The Spread Function

An important feature of any algorithm for embedding watermarks in thetime domain, is the choice of bit positions of the samples in the audiofile that are to be used for storing the watermark. If the bit positionsthat contain the watermark data are not sufficiently spread out, aprocess analogous to “signal jamming” can be used to erase thewatermark. For example, using only the least significant bits in therespective audio file for storing the watermark is attractive, since theaudio quality will not be perceptibly affected by the watermark.However, the predictability of such an approach exposes the protectedaudio signal to an “erasing” attack that, when directed to the leastsignificant bits, will also affect the quality of the audio signal onlymarginally. However, the use of more significant bit positions ofselected samples for the watermark will perceptibly degrade the audioquality of the original file.

The described method relies on choosing a weighted mix of bit positionsfor storing the watermark. In particular, the utilized bit positionsfollow a normal distribution and can be represented by a Gaussian, alsoknown as “normal” or “bell”, curve. As a result, out of the samplesselected for use by the watermark, the number of samples using bitposition i for storing the watermark is exponentially smaller than thenumber of samples using bit position (i-1). Such a ratio offers a goodcompromise between reliability and distortion introduced by thewatermark.

Since linear Pulse Code Modulation (PCM) encoding, where thequantization levels are evenly paced, is the most common technique usedfor sampling music, it is assumed for the present process that theoriginal data file is PCM encoded. However, this is not essential, andthe discussed algorithm can be easily adapted for other time domainencoding techniques.

FIG. 1 illustrates an audio signal 1 as a function of time. FIG. 1 alsoshows Gaussian curves 2 and 3, which are part of a spread functionchosen for embedding a watermark in the audio signal 1. The functionp(k) denotes the audio file samples, while the function w(k) denotesthose of p(k) samples that are selected to hold the watermark. As shownin FIG. 1, and as indicated in step 202 of method 200 of FIG. 2, eachGaussian curve of the spread function is defined by using the followingparameters:

μ—The point in time when the Gaussian curve peaks.

σ—The standard deviation of the Gaussian curve.

N—The interval between audio samples. Only those sample points in thecurve at intervals of N are selected to embed the watermark.

i_(p)—The bit position of the samples used to store the watermark nearthe peak of the curve, i.e. the value of i at time μ.

Parameter μ is chosen to be at one of the points in time when somedistortion would be tolerable to the auditory senses (e.g., when thereis a loud or jarring piece of audio). However, to minimize the effect ofthe watermark itself on the quality of the audio sample, μ should bepositioned at a point in time, when the PCM signal strength is smallerthan a selected level 4, chosen to correspond to a signal strength Sthat is below the local peaks 5 and 6, as shown in FIG. 1. Thus, μshould have a value that is smaller than that of the local peaks withina region defined by a predetermined number of units in either directionfrom the point of interest. The predetermined number of units can eitherbe a constant specific to the audio file, or fine-tuned by the creatorof the audio file for each Gaussian curve that the audio signal carries.The Gaussian curve should avoid regions of low amplitude sincedistortions in these regions are more discernible to the auditorysenses.

The sample interval N is chosen depending on the length of the desiredwatermark that is to be embedded and the frequency of embedding that isdesired. A typical value can be calculated using the formula:

N=(Sampling frequency*bits per sample*x)/y   (1)

where in Eq. (1) the parameters x and y refer to every ‘x’ seconds ofaudio being protected by a watermark of length ‘y’. For example, if itis assumed that every 30 seconds of CD quality audio (44.1 KHz, 16 bitsper sample) needs to be protected by a 40 byte watermark, thenN=(44100*16*30)/40=529200, i.e., one in every 529200 bytes in the audioneeds to be selected for holding the watermark.

The parameters σ and i_(p) are chosen on the basis of an engineeringcompromise between the expected probability for watermark removalattack, and the tolerance to distortions introduced by the watermark.The value chosen for i_(p) also depends on the bits per sample ratio, orthe granularity of quantization, characterizing the digital audio samplethat is to be protected. An audio recording with higher bits per sampleratio can tolerate a higher i_(p). For a given i (say i=2), the largerthe value of σ, the larger will be the number of selected samples usingthe second least significant bit for storing the watermark.

The effect of different spread curve combinations can be experimentallydetermined with the help of a visual drag-and-adjust application programinterface (API) that allows variations of σ, μ, N and i_(p).

Multiple Gaussian curves also can be used across the same audio file tobetter control the above compromise between security and distortion. Forinstance, FIG. 1 shows two Gaussian curves 1 and 2, defining thedistribution of the watermarked audio data. Any intersecting regionbetween adjacent curves 1 and 2 is ignored.

Additional control over the spread function can be obtained byintroducing the functionality of “shift intervals”, as indicated in step204 in FIG. 2. Shift intervals are used in cases where trade offsbetween contrasting requirements is complex and a single combination ofGaussian curves can not provide a satisfactory solution. In this case, ashift interval is superimposed over an area of a Gaussian curves, wherebit positions need adjustment. For each sample point within this area,the bit positions defined by the Gaussian curve are overridden by aparticular bit position defined for the shift interval.

A shift interval is defined by the parameters (t1, t2, v, p), where t1,t2 are the starting and the finishing points in time, v is the value ofi during the time interval t1 to t2, and p is the value of N (period)during that interval. The respective bit positions of points in anyGaussian curve that exists between t1 and t2 are overridden with v. Thecase when v=p=0 results in a blanking interval. Samples falling withinsuch a blanking interval are exempt from carrying watermarkinginformation. This can be used in critical audio regions, where even anoccasional degradation is unacceptable.

The Spread Function Key

The entire information associated with parameters of the Gaussian curvesand the shift parameters included in the spread function can besummarized in a “Spread Key” recorded in a look-up table.

For example, a Spread Key can be represented as G+S in the equationsbelow where

G=({(μ[1], σ[1], N[1], i _(p)[1], t1[1], t2[1]) . . . (μ[k], σ[k], N[k],i _(p) [k], t1[k], t2[k]))}  (2)

and

S={(t1[1], t2[1], v[1], p[1]) . . . (t1[m], t2[m], v[m], p[m]})   (3)

In Eq (2) G is the set of Gaussian curves and in Eq (3) S is the set ofshift intervals within the audio data. The simplest spread functionincludes only one Gaussian curve and no shift intervals. The spread keyin this case is given by Eq (4).

Spread Key=(μ, σ, N, i _(p))   (4)

The additional data necessary for computing the bit position of theselected samples that are to be used for storing watermark informationis the normalized area under the Gaussian curve. This data can be foundin tabulated form in standard text books on statistics and probability.The embedding software stores the tabulated data in memory.

The Watermark Embedding Algorithm

The algorithm to embed the watermark is as follows:

  Choose the spread function parameters (mew, sigma, i_(p)) valid forthis   sample set, and store them in a lookup table for later use by the  decoder.   bit_position_to_embed = 0;  for t = 0 to end_of_sample do {  /* Normalize ‘t’ so that it can index directly into the Gaussian area,   table see step 206 in Fig 2 */   normalized_t = (t−μ)/σ,  area_under_curve = guassian_area_table[normalised_t];   /* Every ‘x’seconds of audio needs to be protected by a watermark    of length ‘y’*/   N = (Sampling_frequency * bits_per_sample * x)/y   /* 0.5 is thearea under each half of the normalized Gaussian curve */   if(((area_under_curve) mod (0.5/i_(p))) == 0) {    if (normalised_t < 0)bit_position_to_embed++;    else bit_position_to_embed−−;   }   if ( thePCM sample at t does not belong to the set of samples with   period N) {   Do not embed   } else if (t belongs to a shift interval) {    Embedthe encrypted watermark using bit positions specified in the    shiftinterval.   } else {    Embed encrypted watermark atbit_position_to_embed of this    sample;   } }

The above pseudo code is illustrated with the functional description inFIG. 2 and the schematic diagram representation of FIG. 3. As indicatedin step 208 in FIG. 2 and path 301 of FIG. 3, for the first half of eachcurve 1 or 2 the bit position used to store the watermark is incrementedwhenever the area to the left of the current time slot t, normalized to(t−μ)/σ (that is obtained from the stored standardized table defining anormalized area of a Gaussian curve) crosses multiples of (0.5/i_(p)).For the second half of the respective curve 1 or 2, shown with path 302of FIG. 3, at each crossing point, the bit position used to store thewatermark is decremented instead. This process is chosen to ensure thatthe number of samples in which bit position i is used to store thewatermark, is exponentially smaller than the number of samples in whichbit position (i-1) is used to store the watermark. To achieve this, thearea under the curve for each bit position, which is 0.5/i_(p), needs toremain the same. The numerator 0.5 is the area under each half of anormalized Gaussian curve (total area is 1), whilst i_(p) is the largestbit position that carries watermarked data. The area under the curve isdistributed uniformly across bit positions used to store the watermark,even though the number of samples where the same bit position is usedfor watermark storage is distributed exponentially.

An encryption algorithm can be used in conjunction with the spreadalgorithm described previously. One example of such algorithm is thewidely used “RC4” (also known as “ARC4” or “ARCFOUR”) stream cipheralgorithm that produces dissimilar cipher text for each instance of thewatermark. The resulting cipher stream is embedded at the bit positionsof chosen samples, as calculated by the spread algorithm describedpreviously.

If a respective Gaussian curve is valid only during a time interval t1to t2, the steps outlined in the above watermark embedding algorithm areapplied only during that interval. The spread parameters can either begenerated automatically by software (by following heuristics and/or withthe help of a random number generator), through user input using acustom drop-and-adjust program interface or by a combination of both.The encoder uses the bit positions of the samples generated above, forstoring the encrypted watermark. Encryption can be accomplished by anyencoding algorithm. After embedding the watermark, the spread keys, theencryption keys and the watermark itself, are stored in a lookup tableto be used later for decoding.

A measure of the relative amount of audio degradation introduced intothe protected audio file by the watermark during any time interval canbe determined with the use of a standardized table defining a normalizedarea of a Gaussian curve, by finding the area under the curve duringthose time intervals.

The proposed method for introducing a spread in the number of bits usedfor embedding a watermark gives good control over watermark positioningwith only limited amount of retrieval information necessary to bestored. To allow verification of the watermark by an authorized party,the decoder of the verifying party needs to access the lookup tableincluding the spread keys, the encryption keys and the watermark. Duringdecoding, the corresponding spread function parameters are obtained fromthe lookup table and the spread function is reconstructed. Watermarkbits from the identified bit positions are continuously extracted andfed into the stream decipher along with the decryption key that is alsoobtained from the lookup table. The watermark information is extractedfrom the audio file and compared with the watermark information storedfor this audio work in the lookup table, to effect verification of theauthenticity of the watermark.

The watermark embedding or extraction can be accomplished in a singlepass of the audio data through an audio data processing system thatdecodes the coded data and verifies the watermark. Of course, if thespread function is present only over part of the audio data, only thatpart of the audio data needs to be processed. The described method foridentifying the bits for embedding the watermark allows the watermarkencoding or decoding at high speeds using simple mathematicaloperations. Notably, the method described herein makes it difficult formalicious attacks to successfully erase or replace the watermark.

Computer Platform

FIG. 4 shows a schematic block diagram of a network system 400 withwhich the method for selecting the bits for embedding watermarks, asdescribed above with respect to FIGS. 1 to 3, can be implemented in theform of application programs executable within a general purposecomputer system 401 or within a hand-held device 425. The softwareimplementing the method described with the pseudo code in the “TheWatermark Embedding Algorithm” section, and any other associatedsoftware, may be stored in a computer readable medium including storagedevices. In the case illustrated in FIG. 4, the software is loaded intothe computer 401 from the computer readable medium 410 and then executedby the computer 401. A computer readable medium having such software orcomputer program recorded on it is a computer program product. As seenin FIG. 4, the computer system 401 can include input devices such as akeyboard 402 and a mouse pointer device 403, and output device such asdisplay device 414. In this configuration, the computer 401 can beconnected to any other computer systems via a network as data conversionis a means usually utilized when the watermark or the spread key dataneeds to be used by multiple computer systems, communicating with eachother over a network. An external Modulator-Demodulator (Modem)transceiver device 416 may be coupled to the computer 401 forcommunicating to and from a communications network 420 via a connection421. The network 420 may be a wide-area network (WAN), such as theInternet, or a private LAN.

The computer 401 typically includes at least one processor unit 405, anda memory unit 406 for example formed from semiconductor random accessmemory (RAM) and read only memory (ROM). Here, the processor unit 405 isan example of a processing means which can also be realized with otherforms of configuration performing similar functionality. The computer401 also includes an number of input/output (I/O) interfaces including avideo interface 407 that couples to the video display 414, an I/Ointerface 413 for such devices like the keyboard 402 and mouse 403, andan interface 408 for the external modem 416. In some implementations,the modem 416 may be incorporated within the computer 401, for examplewithin the interface 408. The computer 401 may also have a local networkinterface 411 which, via a connection 423, permits coupling of thecomputer 401 to a local computer network 422, known as a Local AreaNetwork (LAN). As also illustrated, the local network 422 may alsocouple to the wide network 420 via a connection 424, which wouldtypically include a so-called “firewall” device or similarfunctionality. The interface 411 may be formed by an Ethernet™ circuitcard, a wireless Bluetooth™, an IEEE 802.11 wireless arrangement or acombination of thereof.

Storage devices 409 are provided and typically include a hard disk drive(HDD) 410. It should be apparent to a person skilled in the art thatother devices such as a floppy disk drive, an optical disk drive and amagnetic tape drive (not illustrated) may also be used. The components405 to 413 of the computer 401 typically communicate via aninterconnected bus 404 and in a manner which results in a conventionalmode of operation of the computer 401.

Typically, the programming modules that incorporate the method forchoosing the bit positions for watermarking are resident on the storagedevice 409 and read and controlled in execution by the processor 405.Storage of intermediate product from the execution of such programs maybe accomplished using the semiconductor memory 406, possibly in concertwith the storage device 409. In some instances, the application programsmay be supplied to the user encoded on one or more CD-ROM or other formsof computer readable media and read via the corresponding drive, oralternatively may be read by the user from the networks 420 or 422.

If verification is required on the handheld device 425, it can eitherutilize its own storage and processing means, similar to these describedin relation to computer 401, or make use of a wireless networkconnection to a computer system, such as 401, on which all watermarkrelated processing can be carried out remotely.

While the invention has been hereby described by using an example thatis believed to represent the most practical and preferred embodiment, itwould be clear to a skilled addressee that other embodiments andvariations will also be within the scope of the main concept of theinvention. For example, the method for selecting the bit positions ofthe samples used for storing a watermark has been descried here in thecontext of an audio file that is linearly PCM encoded. However, themethod is applicable for other encoding techniques, as well as to videoand other types of digital data in the time domain.

The discussed method for selecting the bit positions of the samples usedfor storing a watermark, allows spreading the watermark in the timedomain using Gaussian curves. This offers a compact spread informationrepresentation. The data processing involved is relatively simple withmodest demands on the computational power of the processing device. Thisfacilitates identifying the location of a watermark in real-time even ina low-MIPS (Millions of Instructions per Second) devices, such as mobilephones and other handheld media players.

Other advantages of the discussed method include the following;

-   -   a) the watermark is spread over the data in such a manner that,        ‘guess’ deletions of the watermark significantly erode the        quality of the watermarked audio file;    -   b) the spread function can be compactly represented in the form        of a spread key. Even if the spread algorithm is known, security        of the watermarked audio file is ensured by the key;    -   c) the original signal data is not needed for watermark        verification;    -   d) the author of the audio work can adjust the algorithm        operation to exploit his/her knowledge of the work that is        getting watermarked;    -   e) Streaming audio can be watermarked on-the-fly and search        crawlers can run the detection algorithm while displaying        results also on-the-fly.

1. A method for protecting digital audio data comprising a plurality ofsamples, the method comprising; selecting bit positions for storing adigital watermark in the digital audio data in time domain, by choosinga spread function characterising the plurality of the selected bitpositions, wherein the spread function comprises at least one Gaussiancurve.
 2. The method of claim 1, wherein the at least one Gaussian curveis defined by spread function parameters including; a) the point of timecorresponding to the peak of the Gaussian curve, b) the standarddeviation of the Gaussian curve; c) the time interval between samplesselected for storing the watermark; and d) the bit position of thesample storing the watermark at the peak of the Gaussian curve.
 3. Themethod of claim 2, wherein the spread function comprises a plurality ofGaussian curves, each characterized by respective parameters a) to d).4. The method of claim 2, the spread function further comprising a shiftinterval, the shift interval having a pre-determined bit position andbeing arranged to at least partially overlap a pre-defined Gaussiancurve of the spread function, wherein data bit positions in the overlaparea are overridden by the pre-determined bit position, to effectstoring the watermark in the overlap area in the pre-determined bitposition specified for the shift interval.
 5. The method of claim 4,wherein the shift interval is defined by; e) duration of the shiftinterval, including the starting and the final point of time; f) a valueof the bit position that is to be used during the shift interval; and g)the value of the time interval between samples selected, as defined inc) in relation to the respective overlapped Gaussian curve.
 6. Themethod of claim 5, wherein both the value of the bit position, from f),and the time interval, from g), are equal to zero, to effect exemptingthe digital audio data within the shift interval from carrying watermarkdata.
 7. The method of claim 5, wherein the spread function isrepresented by a spread key including parameters defined in a) to g),the key being made available for verifying the watermark data.
 8. Themethod of claim 2, wherein the spread parameters a) to d) are at leastpartially generated automatically.
 9. The method of claim 2, wherein thespread parameters a) to d) are at least partially user defined.
 10. Themethod of claim 7, wherein the method comprises: A) for each of theplurality of points in time covered by the spread function, choosing thespread function parameters a) to d), that are valid for the respectivetime intervals in which the respective point in time falls, and storingthe parameters in a spread function key; B) normalising each point intime to index directly into a standardised table defining a normalisedarea of a Gaussian curve; and C) when the normalised area to the left ofthe current time slot, obtained from the table, crosses multiples of onehalf of the inverse value of the largest bit position that carrieswatermarked data, performing; i) for the first half of the Gaussiancurve, incrementing the respective bit position for storing thewatermark, whilst ii) for the second half of the curve, decrementing therespective bit position for storing the watermark.
 11. The method ofclaim 10, the method further comprising; D) for each points in time forwhich a shift interval is applicable, storing the watermark data in thebit position specified in the shift interval; and E) for each remainingpoints in time, storing the watermark data in the bit positionscalculated in claim
 10. 12. The method of claim 10, wherein anencryption algorithm, having an encryption key, is applied to thewatermark, the encryption key, the spread function key and the watermarkitself being stored for use during decoding and copyright verification.13. A stand-alone or a networked computer system for selecting bitpositions for storing a watermark in a digital audio signal comprisingof plurality of samples in time domain, said computer system comprising:computational means for spreading the digital watermark data in timedomain by storing it in bit positions of selected ones of the samples,the computational means being programmed to define a spread function,characterising the plurality of the selected bit positions used forstoring the watermark, that comprises at least one Gaussian curve, theGaussian curve being defined by spread parameters including; a) thepoint of time corresponding to the peak of the Gaussian curve; b) thestandard deviation of the Gaussian curve; c) the time interval betweensamples selected for storing the watermark; and d) the bit position ofthe sample storing the watermark at the peak of the Gaussian curve. 14.A computer program product having a computer readable medium having acomputer program recorded therein for selecting bit positions forstoring a watermark in a digital audio data, comprising of plurality ofsamples, in time domain, said computer program comprising means forspreading the digital watermark data by storing it in bit positions ofselected ones of the samples, wherein a spread function characterisingthe plurality of the selected bit positions used for storing thewatermark comprises at least one Gaussian curve, the Gaussian curvebeing defined by spread parameters including; a) the point of timecorresponding to the peak of the Gaussian curve; b) the standarddeviation of the Gaussian curve; c) the time interval between samplesselected for storing the watermark; and d) the bit position of thesample storing the watermark at the peak of the Gaussian curve.